3(1+a^2+a^4)-(1+a+a^2)^2
=3+3a^2+3a^4-1-a^2-a^4-2a-2a^2-2a^3
=2+2a^4-2a-2a^3
=2[a^3(a-1)-(a-1)]
=2(a-1)(a^3-1)
=2(a-1)(a-1)(a^2+a+1)
=2(a-1)^2[(a+1/2)^2+3/4]
因为(a+1/2)^2+3/4>0
(a-1)^2>=0
所以2(a-1)^2[(a+1/2)^2+3/4]>=0
所以3(1+a^2+a^4)-(1+a+a^2)^2>=0
所以3(1+a^2+a^4)>=(1+a+a^2)^2